Training while exhaustedGood; but was "training while exhausted" ever advised for new techniques in the martial arts? I've only ever heard this approach for a means of removing excess/waste movement from a well understood technique as a means of absorbing the principles. The criticism of crossfit is relevant for Fitness.SE, but is it non-sequiter for MA.SE?

Short leg issue and wide-soled shoePersonal views of chiropractics aside, hip alignment could be a factor. Either way, a podiatrist may be able to prescribe a custom orthotic to help your rather unique situation.

How should a novice train if unable to join a dojo yet?Moving doesn't necessarily mean you can't train in a dojo. Find an art you're interested in, then go and look at google maps for training in the last few locations. If you have time to run or exercise, you can find time to train. If you want to learn a martial art, study it; if you just want to get in shape, you can join a gym!